The study of the behavior of gases has multiple applications; from the way our bodies inhale and exhale air to [insert another application here]. This behavior has been studied through thorough experimentation. An useful finding from these experiments is that the behavior of gases in relation with pressure, volume, temperature, and amount, sometimes follows a linear trend. It is seen especially at low pressures and high temperatures, and is mathematically represented as the following equation.
This is called the ideal gas equation. Here, P is the pressure in Pa, V is the volume in m3, n is the number of moles, T is the temperature in Kelvin, and k is the ideal gas constant, which has a known value of 1.3806488 x 10-23.
Several simpler gas laws arise from the ideal gas law. Two of these are Boyle’s Law and Charles’ Law. Each of these describes the relationship between two of the variables described in the ideal gas equation. Robert Boyle discovered that under certain conditions, volume and pressure follow an inversely proportional relationship. Mathematically,
where Cb is equal to nkT. This is known as Boyle’s Law.
Charles’ Law describes that the volume of a gas is directly proportional to the temperature. Mathematically,
where Cc is equal to nk/P.
The goal of the experiment is to verify Boyle’s and Charles’ Law through the calculation of the volume of an airtight chamber by plotting the relationship between volume and pressure, and volume and temperature.
The materials used in the experiment were a heat engine, an air chamber can, rubber tubings, a Vernier LabQuest with a gas pressure sensor, a thermocouple, some ice, a pot, and a gas stove.
First, the pot was filled with water and placed on the stove to boil. For the verification of Boyle’s Law, the air chamber can was connected to the heat engine using rubber tubing, then submerged in the pot filled with boiling water. The piston of the heat engine was lifted to its maximum height, then the gas pressure sensor to the Vernier LabQuest. The initial pressure reading was then recorded. The temperature was also recorded using a thermocouple. Masses were then placed on the piston, in increasing increments of 50g. As each increment of mass was added, the change in height of the piston was recorded. Because the diameter of the piston is already known, the change in volume may be calculated. This was plotted against the change in pressure in the piston. The graph may be seen below.
From the high R2 value, it is evident that the relationship between pressure and volume is indeed quite linear. For this part of the experiment, the slope of the equation is equal to 1/nkT, and the volume of the air chamber itself is theoretically equal to the quotient of the y-intercept and the slope. By calculation, the number of moles in the chamber was 1.12 x 1019, and the volume of the air chamber was 4.74 x 10-4 m3.
These results were then compared to those obtained from a set of procedures involving Charles’ Law instead. The pot was removed from the stove, and instead of increasing the pressure on the piston, several chunks of ice were added to the pot, and the change in temperature was measured against volume. The graph of the results is shown below.
For this test, the number of moles is equal to the product of the slope and the recorded pressure divided by k, while the volume of the air chamber is simply equal to the y-intercept. The results of both experiments are tabulated below.
The deviation between the two values for the number of moles is quite large, but for the volume of the air chamber it is quite close. This makes sense, as the sheer largeness of numbers involved in measuring the number of moles makes it more prone to larger differences in data. However, on a whole, the experiment may deemed successful considering the error-prone set-up.
Sources of error include: improperly sealed connections of rubber tubing, inconsistent pressure and temperature readings, the fact that the system was an open one and heat could escape at any time, and limitations in the measurement of volume due to a relatively unclear scale on the piston.